We consider power distribution networks containing source nodes producing electricity and nodes representing electricity consumers. These sources and these consumers are interconnected by a switched network. Configuring this network consists in deciding which switches are activated and the orientation of the links between these switches, so as to obtain a directed acyclic graph (DAG) from the producer nodes to the consumer nodes. This DAG is valid if the electric flow it induces satisfies the demand of each consumer without exceeding the production capacity of each source and the flow capacity of each switch. We show that the problem of deciding if such a valid DAG exists is NP-complete. In the case where such a valid DAG exists, we study the problem of determining a valid DAG that balances the ratio between the amount of electricity produced and the maximum production capacity for each source. We show that this minimization problem is also NP-complete in the general case but that it becomes polynomial in the case of ring network topologies.